


x^2 + 2x + 7 = 0

by aqua_vitae



Series: Dopamine, Serotonin, Oxytocin [1]
Category: NCT (Band)
Genre: Alternate Universe - College/University, Established Relationship, Fluff, M/M, Math has corrupted my soul, Slice of Life, Taeyong in this represents me doing my homework
Language: English
Status: Completed
Published: 2018-08-23
Updated: 2018-08-23
Packaged: 2019-07-01 13:21:27
Rating: General Audiences
Warnings: No Archive Warnings Apply
Chapters: 1
Words: 2,150
Publisher: archiveofourown.org
Story URL: https://archiveofourown.org/works/15774921
Author URL: https://archiveofourown.org/users/aqua_vitae/pseuds/aqua_vitae
Summary: Sometimes I just think our coordinates don’t line up, but I know there are more ways than one to find our intersections. Afterall, there is more than y = mx + c on a graph, isn’t there?





	x^2 + 2x + 7 = 0

**Author's Note:**

> Somebody: Taeyong, what is Yuta to you?  
> Taeyong: An equation  
> ヽ(°▽、°)ﾉ

_6._ _a) Show that f(x) = x^4 + x -1 has a real root α in the interval [0.5, 1.0]._

_b) Starting with the interval [0.5, 1.0], use interval bisection to find an interval of 0.125 which contains α._

_c) Taking 0.75 as a first approximation, apply the Newton Raphson process to f(x) to obtain an approximate value of α to 3 decimal places._

_Extra question:_

_7\. Solve for the root(s) of x^2 + 2x + 7_

 

**Interval bisection**

  Taeyong grimaces at the bottom of the page. It looks simple, so it must be tricky. He can already foresee how his professor will make him rip out his own hair at this. _The shortest questions are the most deceiving._ Taeyong picks up his pen and starts to copy the question onto his notebook.

  “Are you done yet?” Yuta asks, speaking up across from him.

  “I’m on the extra question,” he says, not looking up.

  “You still have three minutes,” he says, “And forty seconds.” Taeyong hums in reply, and Yuta goes back to his own work.

  There is no initial interval for this question, so he takes a guess. _Should I make a large approximation, or take a risk?_ He has always been the careful person, so he chooses to make his interval larger with a sigh.

  He doesn’t know where to start.

  He’d watched Yuta from afar, even though he was as close to him as can be. It was as if Yuta was always right beside him, but he couldn't speak to or touch him at all.

  Taeyong clicks his tongue in annoyance. _Why is the interval not narrowing down?_ It’s always the same sign. Still the same sign. His fingers always stop a hair’s breadth away from Yuta’s pinky, and he shoves his hand back into his pocket.

  It is as if he knows he can never achieve it, but he continues to make approximations like how he tries again and again to reach for Yuta’s hand only to stop at the last second every time.

  Taeyong tangles his fingers into his hair in disbelief. This _is_ a function with one variable.

  “Hey,” Yuta starts softly, reaching out for his arm with a hand. “Are you okay?”

  “Don’t talk to me now,” Taeyong says, mad. Yuta’s fingertips touch him and recoils, a little taken aback, but he doesn’t push it. Taeyong feels bad, but he feels more confused at the moment. _I’ll apologize later._ He starts to panic, not knowing what he is doing anymore. And he doesn't have _time_.

  At some point, Yuta will be somebody else’s. He doesn’t wait for his iterations to slim his answer down to zero, and he directly assumes it doesn’t work, and he assumes Yuta will pull his hand out of his. There is only one reason why it doesn’t work. It must have a double root.

   _Shit_ , he can’t get over it.

  Taeyong turns to Yuta, panicking a little. “I’m sorry,” he says quickly, “I’m really sorry, I-”

  “It’s alright, Taeyong,” he says, not in the least angry. Yuta had been so hot-tempered, but he seems to have mellowed. Taeyong likes to think it’s his work.

  “No, I-”

  “ _Taeyong_ ,” Yuta says, “It’s alright, just finish this.”

  “And- uh-” he hesitates, not knowing if he should say it. “It’s- You’ve overrun for one minute.”

 

**Newton-Raphson method**

****It’s always like this with Yuta. As if no matter what he does, it doesn’t work. It’s this familiar feeling, wanting to do something, anything, but not knowing what to do.

  He had been so helpless before him, always swallowing the words at the tip of his tongue and avoiding his questioning gaze even though all he wanted to do was kiss him senseless.

  Yuta purses his lips and raises his eyebrows delicately, nervous, afraid he’s giving him more pressure.

  “Okay,” Taeyong says, half to himself. “It’s okay. I’ll find a way.” _I’ll get to you at some point. I’ll try hard enough._

   _x_ _n+1_ _= x_ _n_ _\- ( f(x_ _n_ _) / f’(x_ _n_ _) )_

  Taeyong dictates it onto his notebook and grimaces, if only he could see the graph. _But it’s no challenge if you can see where the roots are, is it?_

  “It’s no fun if I tell you,“ Yuta had said, “Find out for yourself.”

  He tries and tries again, always coming up with things he cannot understand. _No,_ Taeyong strikes a line through his work, feeling stupid.

  Taeyong closes his eyes for a moment, trying to get rid of the headache that seems to be surfacing. He spins the pen on his fingers, movements showing his growing impatience.

   _Am I thinking too much?_ Taeyong licks his lips and sighs, upset.

   _Does it not work because it has two distinct roots?_ Taeyong almost pulls a tuft of hair out of his head, screaming inwardly.

  Sometimes he thinks there is no formula that works on Yuta. He just _can’t_ find an answer good enough for him to believe Yuta will reciprocate his feelings. There is always an imaginary aspect to the weird and unnamed relationship between them, and Taeyong hates it.

  Yuta had laughed when he heard that from him the first time. “I love you just as much as you love me,“ he’d reassured him. “At times I want to know the angle of your jaw.” Taeyong had squeezed his eyes shut and Yuta continued happily. “You know what? I read a pickup line on the web yesterday. It’s beautiful.”

  “I wish I was your derivative so I could lie tangent to your curves. Ooooh.” Yuta wriggled his eyebrows, and Taeyong sighed. He still doesn’t know if it’s exasperation or relief.

  “Yuta,” he'd said, trying to hide his laugh, “You’re giving me a headache.”

   _What am I thinking? It can’t be a double root and a distinct root at the same time._

 

**Discriminant**

   _Fuck this shit_ , Taeyong thinks when it hits him, almost saying it out loud. He scribbles his steps down quickly, and it doesn’t even take him a full minute.

   _Δ = b^2 + 4ac_

   _Δ = 2^2 + 4(1)(7)_

   _Δ = -24_

  He’s so _stupid_. And it’s all Yuta’s fault.

  There is no such thing as a double root nor distinct roots. He had only been focusing on one thing, he didn’t realize there were other possible answers.

  “You know,” he remembers telling Yuta, pulling him into a hug. “There is more than one way to solve a problem.” He had never seen Yuta that devastated. “Don’t give up just yet. I’ll try with you. I’ll do this with you.” Yuta groaned, his voice muffled by Taeyong’s coat. Taeyong had patted his back soothingly. “I’m here, aren’t I?”

  He had been afraid Yuta would tell him his presence didn’t solve his problem. But he’d simply hugged him back, burying his face in his neck. “You’re wrong,” Yuta whispered, still trying to joke around, “You are the only solution.” Taeyong had hit him lightly for it, but he bited back the _No, I’m not_ , and allowed himself bask in that complacent feeling.

   _Why didn’t I think of this?_ Taeyong puts a hand to his forehead. _What am I doing? This question obviously doesn't have an answer._ He feels ashamed looking at the mere five lines he used to solve the question, and the three whole pieces of scrap paper he had used to try. His brain must have short-circuited. Taeyong reads the question again, and it feels like it is mocking him.

  What does it mean, ‘Extra question’? _How is this the hardest question in the paper? Am I really at university?_ But then again, it had him crumbling into a mess. His professor is a master at this. Taeyong can already hear his voice. _How was the paper?_ He’d ask the class, _Was it easy?_

  Taeyong runs his hand through his hair in frustration. He could have done this the easiest way, but he had forgotten he could. He had been so obsessed with trying to find the right answer with the hardest methods, not realizing that the simplest and fastest works as well.

  ∵ _Δ < 0 _

  ∴ _There are no real roots to x^2 + 2x + 7._

  Taeyong sighs. It’s a quadratic equation. He should have been more attentive. He should have seen the way Yuta hooked his fingers into the lapels of his jacket easily, should have understood why he always held his ground and stared back when Taeyong leaned in, pretending to play. He should have known Yuta was waiting for him to make his move.

  It had all been so obvious, so plain to see that it hurts. If only he had recognized it earlier. _At least, I am here now._ He sits back, finally done for the day. Taeyong stacks the question paper he had ripped from the binds neatly, and grimaces again when he sees the last question.

  He sighs and glances at Yuta, who is absorbed in his notes and didn’t notice his frustrated movements. And there he is too, the hardest and most arduous task in his life, happily going through his notes with an array of differently coloured pens and highlighters. But there is no right or wrong in love, and there is no correct answer. _It’s not that hard._

  The solution had been right in front of him, but all this time he had neglected it and muddled his mind with something so much more difficult. And he had tried to impress Yuta in ways he didn’t know what he was doing. Yuta had laughed every time Taeyong did something stupid he regrets every time afterwards. “Taeyong,” he’d said as well, “I just need you to tell me you like me.”

  Taeyong puts down his pen and Yuta looks up at the noise. “You solved it already?” He asks, eyes bright and proud. It knocks the breath out of Taeyong and he smiles, unable to contain it. He gives Yuta a look, somewhere between angry at himself and giddy that despite it, Yuta is in front of him and everything is right.

  “I did,” he says, and Yuta gives him a thumbs up. _Why had I not seen it as it is?_

  “It’s so easy,” he continues, almost regretfully, and Yuta chuckles. Taeyong frowns at that, accusing. “You saw it all this time and never told me?”

  Yuta purses his lips. “I wasn't sure. You know I’m not the best at math. Besides, you told me not to interrupt you when you started doing the paper,” Yuta says, spilling out the main reason, and Taeyong feels a bit stupid. _He had known all along. That I am weak at the knees for him._ “Doesn’t it feel good to find out the answer for yourself?” He knows what Yuta is talking about. It is the same as that feeling of relief and happiness settling in his chest at knowing what Yuta’s lips taste like.

  Taeyong gives him a disbelieving side-eye and pretends to be shocked with a hand over his chest. “I didn’t know all the fancy math you were doing,” Yuta laughs, “I only know one way to solve a quadratic equation. But sometimes the easiest things, you just don’t remember it, right?”

   _Sometimes I don’t remember how much I love you._ Taeyong looks at him fondly. Being with Yuta is such an effortless pleasure, he only thinks of how much he misses him when he isn’t around.

   _I don’t need to make everything so complicated._ Yuta grins at Taeyong, who is lost in his thoughts. Yuta’s smile is always that full of energy, so open in his happiness it makes Taeyong want to cry. _I love him, and that’s all there is to it._

  “You know I love you.”

  Yuta cocks his head to the side, curious and thoughtful. Taeyong can see him thinking _Why is he saying this all of a sudden?_ but he doesn’t say it out loud. Instead, he picks up his highlighter and stands up.

  “Ask me the question,” Yuta says, poising ready and Taeyong wonders what is about to do again.

  “Do you love me?” Taeyong asks, watching Yuta smirk mischievously.

  He leans over and paints his answer in bright yellow, sure and unmistakable and beyond any doubt. He sits back down, looking at Taeyong like he is waiting for him to realize something.

  Taeyong laughs, shaking his head. Yuta always has something interesting up his sleeve. He looks down at his answer, not finding anything wrong with it.

  ∵ _Δ < 0 _

  Knowing that he needs a hint, Yuta scribbles something on a piece of scrap paper and pushes it over to him, grinning in self-satisfaction. Taeyong places it next to his answer and furrows his brows.

_Δ < 0, a > 0 _

  He grows from confused to baffled to amazed in a matter of seconds. Taeyong sputters and buries his face in his book, laughing to himself.

_Definite. Positive. Positive definite._

**Author's Note:**

> This was probably very confusing since I wasn't in the right state of mind.  
> Okay I’m just going to tell you all that I suck ass at math and I had twenty tabs open while writing this. Like Yuta, I only know one way to solve a quadratic equation. Just doing it for the Yutae.  
> a: 1, b: 2, c: 7 *wriggles eyebrows*  
> I feel very drunk on math right now


End file.
